Locally variable turbulent Prandtl number considerations on the modeling of Liquid Rocket Engines operating above the critical point

The general idea behind the present work is to study the injection of a cryogenic liquid numerically into rocket engines, where propellant conditions are above the thermodynamic critical point, for a non-reactive case. The singular behavior of thermodynamic and transport properties at and around the critical point makes this a most challenging task. While mass diffusivity, surface tension, and latent heat are zero at the critical point, isentropic compressibility, specific heat, and thermal conductivity tend to infinity. As a result, the distinction between liquid and solid phases disappears. Ultimately, the fluid has liquid-like density and gas-like properties, mass diffusion replaces vaporization as a governing parameter, and it dominates over jet atomization. Henceforth, any model used incorporates as close as possible to reality, the variation of thermodynamic and transport properties. An incompressible variable-density flow is simulated using Favre averages (FANS) with a locally variable turbulent Prandtl number, taking into account the potential core, transition, and the self-similar region of the jet. The use of a turbulence model with a variable turbulent Prandtl number arises from the ineffectiveness in predicting observed anisotropies in the thermal eddy diffusivity fields when this value is taken as a constant. Favre averaged conservation equations for mass, momentum, and energy are coupled with the k- two-equation turbulence model and discretized following the third order upwind QUICK scheme. Stability and accuracy of the results are maintained through a careful selection of the parameters involved in the models. The use of the conservation equation for energy is justified as an indirect means to evaluate the thermal field. Results are compared with experimental cases for validation purposes as well as LES computations for performance comparison and evaluation of the degree of model complexity needed to achieve satisfactory results.